Soft Gluon Logarithmic Resummation and Hadron Mass Effects in Single Hadron Inclusive Production

We define a general scheme for the evolution of fragmentation functions which resums soft gluon logarithms in a manner consistent with fixed order evolution. We present an explicit example of our approach in which double logarithms are resummed using the Double Logarithmic Approximation. We show that this scheme reproduces the Modified Leading Logarithm Approximation in certain limits, and find that after using it to fit quark and gluon fragmentation functions to experimental data,a good description of the data from the largest x values to the peak region in ln (1/x) is obtained. In addition, we develop a treatment of hadron mass effects which gives additional improvements at small x.